Ambiguous and multifaceted queries widely exist in academic and commercial search engines. Identifying the popular subtopics of queries is an important issue for search engines. In this paper, we propose a novel method to discover the popular subtopics for a given query. Our method first constructs a search behavior tripartite graph based on the search log data. Then, we utilize a subtractive initialized Non-negative Sparse LSA model to mine subtopics from the tripartite graph. The experimental results on two real-world Chinese search logs (i.e., the CADAL search log and the Sogou search log) show that our proposed method can significantly outperform the other comparison methods in term of MAP, £\-nDCG and S-recall. We also applied our method into the CADAL digital library to provide a novel faceted book search service which can reduce the users¡¦ efforts in finding books.